A .25 g chunk of sodium metal is cautiously dropped into a mixture of 50g of water and 50 g of ice both at 0 C 

2Na(s) + 2h2o(l) -> 2naoh(aq) + H2

Delta H = -368 kj

Will the ice melt
Assuming the final mixture has a heat capacity of 4.18 J/g C calculate the final temperature 

The enthalpy of fusion for ice is 6.02 kj/mol

To determine if the ice will melt, we need to calculate the amount of heat released or absorbed during the reaction between sodium and water/ice mixture.

1. First, we need to calculate the heat released by the reaction. We know the enthalpy change (ΔH) for the reaction is -368 kJ.

2. The amount of sodium reacted is 0.25 g. To calculate the moles of sodium (Na), we use the molar mass of sodium (22.99 g/mol).

Moles of Na = Mass of Na / Molar mass of Na
= 0.25 g / 22.99 g/mol

3. From the stoichiometry of the balanced equation, we can see that 2 moles of sodium react with 2 moles of water (H2O). Therefore, the moles of water reacted is the same as the moles of sodium.

4. Now, we can calculate the heat released per mole of water reacted.

Heat released per mole of water = ΔH / Moles of water reacted

5. To find the total heat released for the given amount of water, we multiply the heat released per mole of water by the moles of water reacted:

Total heat released = Heat released per mole of water x Moles of water

6. Since there is a mixture of water and ice, we need to account for the heat absorbed during the transformation of ice into water. The enthalpy of fusion for ice is given as 6.02 kJ/mol.

7. We can calculate the moles of water formed from the ice using the molar mass of water (H2O). For every 18 grams of water formed, 6.02 kJ of heat is absorbed.

Moles of water formed = Mass of ice / Molar mass of water

Here, the mass of ice is 50 g, so we can calculate the moles of water formed.

8. Now, we can calculate the heat absorbed during the melting of ice:

Heat absorbed = Moles of water formed x Enthalpy of fusion

9. Finally, we compare the total heat released with the heat absorbed to determine if the ice will melt. If the total heat released is greater than or equal to the heat absorbed, the ice will melt.

10. To calculate the final temperature of the mixture, we need to use the formula:

Q = mcΔT

where Q is the heat exchanged, m is the mass of the mixture, c is the specific heat capacity, and ΔT is the change in temperature.

Rearranging the formula, we can solve for ΔT:

ΔT = Q / (mc)

Here, Q is the total heat released, m is the mass of the mixture (100 g), and c is the specific heat capacity (4.18 J/g°C) of the mixture.

Plug in the values to calculate the final temperature using the equation for ΔT.

To answer your question, we need to calculate the energy released by the reaction and compare it to the energy required to melt the ice.

Step 1: Calculate the moles of sodium (Na) used.
Using the molar mass of sodium (22.99 g/mol), we can calculate the moles:
0.25 g Na * (1 mol Na / 22.99 g Na) = 0.01087 mol Na

Step 2: Calculate the energy released by the reaction.
Using the balanced equation, we can see that 2 moles of Na produce 368 kJ of energy. Therefore, 0.01087 mol Na will produce:
Energy released = 0.01087 mol Na * (368 kJ / 2 mol Na) = 1.99416 kJ

Step 3: Determine the energy required to melt the ice.
The enthalpy of fusion for ice is given as 6.02 kJ/mol. Since we have 50 g of ice, we can calculate the moles of ice present:
50 g ice * (1 mol ice / 18.02 g ice) = 2.77577 mol ice
Subsequently, the energy required to melt the ice is:
Energy required = 2.77577 mol ice * (6.02 kJ / 1 mol ice) = 16.70783 kJ

Step 4: Compare the energy released with the energy required.
To determine if the ice will melt, we compare the two energy values:
1.99416 kJ (energy released) < 16.70783 kJ (energy required)

Since the energy released is less than the energy required to melt the ice, the ice will not fully melt.

Step 5: Calculate the final temperature.
To calculate the final temperature, we use the equation:
Q = mcΔT

Where:
Q = heat transferred (in J)
m = mass of the water + ice (in g)
c = specific heat capacity of the mixture (in J/g°C)
ΔT = change in temperature (final temperature - initial temperature)

Given:
Initial temperature = 0°C
Mass of water + ice = 50g + 50g = 100g
Specific heat capacity = 4.18 J/g°C

Q = 100g * 4.18 J/g°C * ΔT
1.99416 kJ * (1,000 J / 1 kJ) = 100g * 4.18 J/g°C * ΔT
1994.16 J = 418g°C * ΔT
ΔT = 1994.16 J / 418g°C
ΔT ≈ 4.77°C

The final temperature will be approximately 4.77°C.